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Nate predicted that voter turnout for the next citywide election will be $23\%$ , with a margin of error of $3\%$ . Which of the following represents the plausible range of voter turnout based on Nate's prediction and margin of error? $\newline$ Choose $1$ answer: $\newline$ (A) Between $20\%$ and $26\%$ $\newline$ (B) Between $21.5\%$ and $24.5\%$ $\newline$ (C) Between $23\%$ and $26\%$ $\newline$ (D) Between $23\%$ and $29\%$

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Find values of normal variables

Full solution

Q. Nate predicted that voter turnout for the next citywide election will be

23\%

, with a margin of error of

3\%

. Which of the following represents the plausible range of voter turnout based on Nate's prediction and margin of error?

\newline

Choose

1

answer:

\newline

(A) Between

20\%

and

26\%

\newline

(B) Between

21.5\%

and

24.5\%

\newline

(C) Between

23\%

and

26\%

\newline

(D) Between

23\%

and

29\%

Understand the problem: Understand the problem. $\newline$ Nate predicted a voter turnout of $23\%$ with a margin of error of $3\%$ . The margin of error means that the actual turnout could be $3\%$ higher or lower than the predicted $23\%$ .
Calculate lower limit: Calculate the lower limit of the range. $\newline$ To find the lower limit, subtract the margin of error from the predicted percentage. $\newline$ Lower limit $= \text{Predicted percentage} - \text{Margin of error}$ $\newline$ Lower limit $= 23\% - 3\%$ $\newline$ Lower limit $= 20\%$
Calculate upper limit: Calculate the upper limit of the range. $\newline$ To find the upper limit, add the margin of error to the predicted percentage. $\newline$ Upper limit = Predicted percentage + Margin of error $\newline$ Upper limit = $23\% + 3\%$ $\newline$ Upper limit = $26\%$
Define the range: Combine the lower and upper limits to define the range. $\newline$ The plausible range of voter turnout is between the lower limit and the upper limit. $\newline$ Range = Between $20\%$ and $26\%$

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